Wan Rozali, Wan Nur Fairuz Alwani and Vivaldi, Franco (2018) Nonlinear rotations on a lattice. Journal of Difference Equations and Applications, 24. pp. 1074-1104. ISSN 1023-6198 E-ISSN 1563-5120
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Abstract
We consider a prototypical two-parameter family of invertible maps of Z2, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map of the torus, in the limit of fine discretisation. We prove that there is a set of full density of points which,depending of the parameter values,are either periodic or escape to infinity. The proof is based on the analysis of an interval-exchange map over the integers, with infinitely many intervals.
Item Type: | Article (Journal) |
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Additional Information: | 8818/72019 |
Uncontrolled Keywords: | Arithmetic dynamics; stability; periodic orbits |
Subjects: | Q Science > QA Mathematics > QA300 Analysis |
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): | Kulliyyah of Science > Department of Computational and Theoretical Sciences Kulliyyah of Science |
Depositing User: | Dr Wan Nur Fairuz Alwani Binti Wan Rozali |
Date Deposited: | 20 Jun 2019 09:16 |
Last Modified: | 20 Jun 2019 09:16 |
URI: | http://irep.iium.edu.my/id/eprint/72019 |
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